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\title{Corporate Diversification and Debt Maturity}

\author{\textsc{Enrico Onali and Xiaoxia Ye} \thanks{Onali (E.Onali@bristol.ac.uk) is with the University of Bristol Business School and Ye (Xiaoxia.Ye@nottingham.ac.uk) is with the University of Nottingham, Nottingham University Business School. We are grateful to the editor, Jarrad Harford, and an anonymous referee for their constructive comments and suggestions, which significantly improved the paper. We thank Renée B Adams, Artur Doshchyn, Winston Dou, and Chendi Zhang for their useful comments and suggestions on an earlier version of this paper, and Emmanuel Alanis for share with us the debt overhang data of \citet{alanis2018shareholder}. We also thank conference participants at the International Risk Management Conference and seminar participants at the University of Exeter.}}

\date{Forthcoming in \textit{Journal of Financial and Quantitative Analysis}}
\keywords{Corporate diversification, Debt overhang, Debt maturity, Diversification discount}
\jel{G32, G34, G13}

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\begin{document}
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\thispagestyle{empty}
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\justifying


\clearpage
\tikzstyle{bag} = [text width=2em, text centered]
\tikzstyle{end} = []
\begin{figure}[t]
	\begin{center}
		\caption{Timeline of the possible paths of stand-alone firm $S$'s assets-in-place}
		\label{fig:fs_aip}    
		\begin{justify}
			{\small This figure plots all possible values of stand-alone firm $S$'s assets-in-place on $t=2$ and two states $\{ G \text{ and } B\}$ on $t = 1$. The probability of each path is shown along the path. Long-term and short-term face values of debt are indicated in the graph as long and short lines with corresponding legends.}
		\end{justify}
		\begin{tikzpicture}[sloped]
			\node (t0) at ( 0,0) [bag] {$F_s$};
			\node (t1_d) at ( 4,-1.5) [bag] {$B$};
			\node (t1_u) at ( 4,1.5) [bag] {$G$};
			\node (t2_u) at ( 8,5) [bag] {$24$};
			\node (t2_m) at ( 8,0) [bag] {$12$};
			\node (t2_d) at ( 8,-5) [bag] {$0$};
			\node (t_0) at (0, -6) [align=left]{$t = 0$};
			\node (t_1) at (4, -6) [align=left]{$t = 1$};
			\node (t_2) at (8, -6) [align=left]{$t = 2$};
			\node (st_fv) at (4.5, -1.3125) [align=left]{};
			\node (lt_fv) at (8.5, 0.3125) [align=left]{};
			\draw [-stealth] (t0) to node [above] {\small $p=\frac{1}{2}$} (t1_d);
			\draw [-stealth] (t0) to node [above] {\small $p=\frac{1}{2}$} (t1_u);
			\draw [-stealth] (t1_u) to node [above] {\small $\left.p=\frac{1}{2}\right|G$} (t2_u);
			\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{3}\right|G$} (t2_m);
			\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{6}\right|G$} (t2_d);
			\draw [-stealth] (t1_d) to node [below] {\small $\left.p=\frac{1}{2}\right|B$} (t2_d);
			\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{3}\right|B$} (t2_m);
			\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{6}\right|B$} (t2_u); 
			\draw [color=gray](t_0) to node [above] {} (t_1); 
			\draw [color=gray] (t_1) to node [above] {} (t_2);
			\draw [color=magenta] (0.5, -1.3125) to node [above, midway] {\small Short-term debt = $8.5$} (st_fv);
			\draw [color=magenta] (0.5, 0.3125) to node [above left] {\small Long-term debt = $12.75$} (lt_fv);
		\end{tikzpicture}    
	\end{center}
\end{figure}

\begin{landscape}
	\begin{figure}[t]
		\caption{Timeline of the possible paths of multi-division firm $M$'s assets-in-place}
		\label{fig:fm_aip}
		\begin{justify}
			{\small In this figure, panels (a) and (b) plot all possible values of multi-division firm $M$'s two assets-in-place $F_m(1)$ and $F_m(2)$, respectively, on $t=2$ and two states $\{ G \text{ and } B\}$ on $t = 1$. The probability of each path is shown along the path. Panel (c) plots the same paths for the combined assets-in-place $F_m$ for firm $M$. Long-term and short-term face values of debt are indicated in panel (c) as long and short lines with corresponding legends.}
		\end{justify}
		\begin{subfigure}{0.6\textwidth}
			\caption{First assets-in-place: $F_m(1)$}
			\label{fig:fm_aip_1}
			\begin{center}
				\scalebox{0.9}{
					\begin{tikzpicture}[sloped]
						\node (t0) at (0,0) [align=left] {$F_m(1)\text{  }$};
						\node (t1_d) at ( 4,-1.5) [bag] {B1};
						\node (t1_u) at ( 4,1.5) [bag] {G1};
						\node (t2_u) at ( 8,5) [bag] {12};
						\node (t2_m) at ( 8,0) [bag] {6};
						\node (t2_d) at ( 8,-5) [bag] {0};
						\draw [-stealth] (t0) to node [below] {\small $p=\frac{1}{2}$} (t1_d);
						\draw [-stealth] (t0) to node [above] {\small $p=\frac{1}{2}$} (t1_u);
						\draw [-stealth] (t1_u) to node [above] {\small $\left.p=\frac{1}{2}\right|G1$} (t2_u);
						\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{3}\right|G1$} (t2_m);
						\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{6}\right|G1$} (t2_d);
						\draw [-stealth] (t1_d) to node [below] {\small $\left.p=\frac{1}{2}\right|B1$} (t2_d);
						\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{3}\right|B1$} (t2_m);
						\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{6}\right|B1$} (t2_u);        
					\end{tikzpicture}
				}        
			\end{center}
		\end{subfigure}
		\hfill
		\begin{subfigure}{0.6\textwidth}
			\caption{Second assets-in-place: $F_m(2)$}
			\label{fig:fm_aip_2}    
			\begin{center}
				\scalebox{0.9}{
					\begin{tikzpicture}[sloped]
						\node (t0) at (0,0) [align=left] {$F_m(2)\text{  }$};
						\node (t1_d) at ( 4,-1.5) [bag] {B2};
						\node (t1_u) at ( 4,1.5) [bag] {G2};
						\node (t2_u) at ( 8,5) [bag] {12};
						\node (t2_m) at ( 8,0) [bag] {6};
						\node (t2_d) at ( 8,-5) [bag] {0};
						\draw [-stealth] (t0) to node [below] {\small $p=\frac{1}{2}$} (t1_d);
						\draw [-stealth] (t0) to node [above] {\small $p=\frac{1}{2}$} (t1_u);
						\draw [-stealth] (t1_u) to node [above] {\small $\left.p=\frac{1}{2}\right|G2$} (t2_u);
						\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{3}\right|G2$} (t2_m);
						\draw [-stealth] (t1_u) to node [below] {\small $\left.p=\frac{1}{6}\right|G2$} (t2_d);
						\draw [-stealth] (t1_d) to node [below] {\small $\left.p=\frac{1}{2}\right|B2$} (t2_d);
						\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{3}\right|B2$} (t2_m);
						\draw [-stealth] (t1_d) to node [above] {\small $\left.p=\frac{1}{6}\right|B2$} (t2_u);        
					\end{tikzpicture}
				}       
			\end{center} 
		\end{subfigure}
	\end{figure}
\end{landscape}

\begin{landscape}
	\begin{figure}
		\ContinuedFloat
		\caption{Timeline of the possible paths of multi-division firm $M$'s assets-in-place (cont.)}
		\begin{center}
			\begin{subfigure}{1\textwidth}
				\caption{Combined assets-in-place $F_m$}
				\label{fig:fm_aip_combined}
				\begin{center}
					\scalebox{1}{
						\begin{tikzpicture}[sloped]
							\node (t0) at (-2,0) [align=right]{\small $~~F_m = F_m(1) + F_m(2)$};
							\node (t1_d) at ( 4,-2.5) [bag] {B1B2};
							\node (t1_m) at ( 3.5,0) [align=left] {\small G1B2 or B1G2};
							\node (t1_u) at ( 4,2.5) [bag] {G1G2};
							\node (t2_1) at ( 8,5) [bag] {24};
							\node (t2_2) at ( 8,2) [bag] {18};
							\node (t2_3) at ( 8,0) [bag] {12};
							\node (t2_4) at ( 8,-2) [bag] {6};
							\node (t2_5) at ( 8,-5) [bag] {0};
							\node (t_0) at (-1, -6) [align=left]{$t = 0$};
							\node (t_1) at (4, -6) [align=left]{$t = 1$};
							\node (t_2) at (8, -6) [align=left]{$t = 2$};
							\node (st_fv) at (4.5, -2.2917) [align=left]{};
							\node (lt_fv) at (8, -0.5417) [align=left]{};
							\draw [-stealth] (t0) to node [above right] {\small $p=\frac{1}{4}$} (t1_d);
							\draw [-stealth] (t0) to node [above]{\small $p=\frac{1}{2}$} (t1_m);
							\draw [-stealth] (t0) to node [above] {\small $p=\frac{1}{4}$} (t1_u);
							\draw [-stealth] (t1_u) to node [above] {} (t2_1);
							\draw [-stealth] (t1_u) to node [above] {} (t2_2);
							\draw [-stealth] (t1_u) to node [above] {} (t2_3);
							\draw [ -stealth] (t1_u) to node [above] {} (t2_4);
							\draw [ -stealth] (t1_u) to node [above] {} (t2_5);
							\draw [ -stealth] (t1_m) to node [above] {} (t2_1);
							\draw [ -stealth] (t1_m) to node [above] {} (t2_2);
							\draw [ -stealth] (t1_m) to node [above] {} (t2_3);
							\draw [ -stealth] (t1_m) to node [above] {} (t2_4);
							\draw [ -stealth] (t1_m) to node [above] {} (t2_5);            
							\draw [ -stealth] (t1_d) to node [above] {} (t2_1);
							\draw [ -stealth] (t1_d) to node [above] {} (t2_2);
							\draw [ -stealth] (t1_d) to node [above] {} (t2_3);
							\draw [ -stealth] (t1_d) to node [above] {} (t2_4);
							\draw [ -stealth] (t1_d) to node [above] {} (t2_5); 
							\draw [color=gray](t_0) to node [above] {} (t_1); 
							\draw [color=gray] (t_1) to node [above] {} (t_2);
							\draw [color=magenta] (-1.5, -2.2917) to node [above, midway] {\small Short-term debt = $8.33$} (st_fv);
							\draw [color=magenta] (-1.5, -0.5417) to node [below left] {\small Long-term debt = $10.38$} (lt_fv);
						\end{tikzpicture}
					}        
				\end{center}
			\end{subfigure}
		\end{center}        
\end{figure}
	
\begin{figure}[t]
\caption{Plots of the numerical examples of $P^{\text{ST}}_s$ and $P^{\text{ST}}_m$}  
\label{fig:Pst_vs_Plt}
\begin{subfigure}{0.5\linewidth}
    \caption{Stand-alone firm $S$}
    \label{fig:Pst_vs_Plt_Fs}
    \begin{center}    
    \input{P_plot_Fs.tex}
    \end{center}
\end{subfigure}
\hskip 10pt
\begin{subfigure}{0.5\linewidth}
    \caption{Multi-division firm $M$}
    \label{fig:Pst_vs_Plt_Fm}
    \begin{center}
    \input{P_plot_Fm.tex}
    \end{center}
\end{subfigure}
\end{figure}
\end{landscape}

\end{document}